Related papers: Symmetry Breaking in Neuroevolution: A Technical R…
Many approaches in machine learning rely on a weighted graph to encode the similarities between samples in a dataset. Entropic affinities (EAs), which are notably used in the popular Dimensionality Reduction (DR) algorithm t-SNE, are…
An applied problem facing all areas of data science is harmonizing data sources. Joining data from multiple origins with unmapped and only partially overlapping features is a prerequisite to developing and testing robust, generalizable…
Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…
The superposition hypothesis states that single neurons may participate in representing multiple features in order for the neural network to represent more features than it has neurons. In neuroscience and AI, representational alignment…
A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…
Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be…
Spontaneous symmetry breaking plays a fundamental role in many areas of condensed matter and particle physics. A fundamental problem in ecology is the elucidation of the mechanisms responsible for biodiversity and stability. Neutral theory,…
In recent years, the integration of Machine Learning (ML) models with Operation Research (OR) tools has gained popularity across diverse applications, including cancer treatment, algorithmic configuration, and chemical process optimization.…
In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…
Adaptive gradient methods such as Adam have gained increasing popularity in deep learning optimization. However, it has been observed that compared with (stochastic) gradient descent, Adam can converge to a different solution with a…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
The symmetry of complex networks is a global property that has recently gained attention since MacArthur et al. 2008 showed that many real-world networks contain a considerable number of symmetries. These authors work with a very strict…
Robustness of machine learning models is critical for security related applications, where real-world adversaries are uniquely focused on evading neural network based detectors. Prior work mainly focus on crafting adversarial examples (AEs)…
For solving pseudo-convex global optimization problems, we present a novel fully adaptive steepest descent method (or ASDM) without any hard-to-estimate parameters. For the step-size regulation in an $\varepsilon$-normalized direction, we…
The non-convexity of the artificial neural network (ANN) training landscape brings inherent optimization difficulties. While the traditional back-propagation stochastic gradient descent (SGD) algorithm and its variants are effective in…
Deep learning models have proven enormously successful at using multiple layers of representation to learn relevant features of structured data. Encoding physical symmetries into these models can improve performance on difficult tasks, and…
In this paper, we analyze the convergence of the alternating direction method of multipliers (ADMM) for minimizing a nonconvex and possibly nonsmooth objective function, $\phi(x_0,\ldots,x_p,y)$, subject to coupled linear equality…
While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient…
Evolutionary algorithms (EAs) simulate natural selection but have two main limitations: (1) they rarely update individuals based on global correlations, limiting comprehensive learning; (2) they struggle with balancing exploration and…
Evolutionary algorithms are metaheuristic techniques that derive inspiration from the natural process of evolution. They can efficiently solve (generate acceptable quality of solution in reasonable time) complex optimization (NP-Hard)…